# Pipes And Cisterns Shortcut Methods

Pipe and Cistern problems are similar to time and work problems. A pipe is used to fill or empty the tank or cistern.

**Inlet Pipe:**A pipe used to fill the tank or cistern is known as Inlet Pipe.

**Outlet Pipe:**A pipe used to empty the tank or cistern is known as Outlet Pipe.

**Some Basic Formulas**

- If an inlet pipe can fill the tank in x hours, then the part filled in 1 hour = 1/x
- If an outlet pipe can empty the tank in y hours, then the part of the tank emptied in 1 hour = 1/y
- If both inlet and outlet valves are kept open, then the net part of the tank filled in 1 hour is

**Some Shortcut Methods**

**Rule 1:**

Two pipes can fill (or empty) a cistern in x and y hours while working alone. If both pipes are opened together, then the time taken to fill (or empty) the cistern is given by

Example

**Rule 2:**

Three pipes can fill (or empty) a cistern in x, y and z hours while working alone. If all the three pipes are opened together, the time taken to fill (or empty) the cistern is given by

Example

**Rule 3:**

If a pipe can fill a cistern in x hours and another can fill the same cistern in y hours, but a third one can empty the full tank in z hours, and all of them are opened together, then

Example

**Rule 4:**

A pipe can fill a cistern in x hours. Because of a leak in the bottom, it is filled in y hours. If it is full, the time taken by the leak to empty the cistern is